國立虎尾科技大學 |

Nonlinear Expectations and Stochastic Calculus under Uncertainty = with Robust CLT and G-Brownian Motion /

紀錄類型:	書目-語言資料,印刷品 : Monograph/item
正題名/作者:	Nonlinear Expectations and Stochastic Calculus under Uncertainty/ by Shige Peng.
其他題名:	with Robust CLT and G-Brownian Motion /
作者:	Peng, Shige.
面頁冊數:	XIII, 212 p. 10 illus.online resource. :
Contained By:	Springer Nature eBook
標題:	Probabilities. -
電子資源:	https://doi.org/10.1007/978-3-662-59903-7
ISBN:	9783662599037

Nonlinear Expectations and Stochastic Calculus under Uncertainty = with Robust CLT and G-Brownian Motion /
Peng, Shige.

Nonlinear Expectations and Stochastic Calculus under Uncertaintywith Robust CLT and G-Brownian Motion /[electronic resource] :by Shige Peng. - 1st ed. 2019. - XIII, 212 p. 10 illus.online resource. - Probability Theory and Stochastic Modelling,952199-3130 ;. - Probability Theory and Stochastic Modelling,76.

Sublinear Expectations and Risk Measures -- Law of Large Numbers and Central Limit Theorem under Uncertainty -- G-Brownian Motion and Itô’s Calculus -- G-Martingales and Jensen’s Inequality -- Stochastic Differential Equations -- Capacity and Quasi-Surely Analysis for G-Brownian Paths -- G-Martingale Representation Theorem -- Some Further Results of Itô’s Calculus -- Appendix A Preliminaries in Functional Analysis -- Appendix B Preliminaries in Probability Theory -- Appendix C Solutions of Parabolic Partial Differential Equation -- Bibliography -- Index of Symbols -- Subject Index -- Author Index.

This book is focused on the recent developments on problems of probability model uncertainty by using the notion of nonlinear expectations and, in particular, sublinear expectations. It provides a gentle coverage of the theory of nonlinear expectations and related stochastic analysis. Many notions and results, for example, G-normal distribution, G-Brownian motion, G-Martingale representation theorem, and related stochastic calculus are first introduced or obtained by the author. This book is based on Shige Peng’s lecture notes for a series of lectures given at summer schools and universities worldwide. It starts with basic definitions of nonlinear expectations and their relation to coherent measures of risk, law of large numbers and central limit theorems under nonlinear expectations, and develops into stochastic integral and stochastic calculus under G-expectations. It ends with recent research topic on G-Martingale representation theorem and G-stochastic integral for locally integrable processes. With exercises to practice at the end of each chapter, this book can be used as a graduate textbook for students in probability theory and mathematical finance. Each chapter also concludes with a section Notes and Comments, which gives history and further references on the material covered in that chapter. Researchers and graduate students interested in probability theory and mathematical finance will find this book very useful.

ISBN: 9783662599037

Standard No.: 10.1007/978-3-662-59903-7doiSubjects--Topical Terms:

527847
Probabilities.

LC Class. No.: QA273.A1-274.9

Dewey Class. No.: 519.2

Nonlinear Expectations and Stochastic Calculus under Uncertainty = with Robust CLT and G-Brownian Motion /
LDR:03595nam a22004335i 4500 001 1009640
003 DE-He213
005 20200704093132.0
007 cr nn 008mamaa
008 210106s2019 gw | s |||| 0|eng d
020 $a 9783662599037 $9 978-3-662-59903-7
024 7 $a 10.1007/978-3-662-59903-7 $2 doi
035 $a 978-3-662-59903-7
050 4 $a QA273.A1-274.9
050 4 $a QA274-274.9
072 7 $a PBT $2 bicssc
072 7 $a MAT029000 $2 bisacsh
072 7 $a PBT $2 thema
072 7 $a PBWL $2 thema
082 0 4 $a 519.2 $2 23
100 1 $a Peng, Shige. $e author. $4 aut $4 http://id.loc.gov/vocabulary/relators/aut $3 1303596
245 1 0 $a Nonlinear Expectations and Stochastic Calculus under Uncertainty $h [electronic resource] : $b with Robust CLT and G-Brownian Motion / $c by Shige Peng.
250 $a 1st ed. 2019.
264 1 $a Berlin, Heidelberg : $b Springer Berlin Heidelberg : $b Imprint: Springer, $c 2019.
300 $a XIII, 212 p. 10 illus. $b online resource.
336 $a text $b txt $2 rdacontent
337 $a computer $b c $2 rdamedia
338 $a online resource $b cr $2 rdacarrier
347 $a text file $b PDF $2 rda
490 1 $a Probability Theory and Stochastic Modelling, $x 2199-3130 ; $v 95
505 0 $a Sublinear Expectations and Risk Measures -- Law of Large Numbers and Central Limit Theorem under Uncertainty -- G-Brownian Motion and Itô’s Calculus -- G-Martingales and Jensen’s Inequality -- Stochastic Differential Equations -- Capacity and Quasi-Surely Analysis for G-Brownian Paths -- G-Martingale Representation Theorem -- Some Further Results of Itô’s Calculus -- Appendix A Preliminaries in Functional Analysis -- Appendix B Preliminaries in Probability Theory -- Appendix C Solutions of Parabolic Partial Differential Equation -- Bibliography -- Index of Symbols -- Subject Index -- Author Index.
520 $a This book is focused on the recent developments on problems of probability model uncertainty by using the notion of nonlinear expectations and, in particular, sublinear expectations. It provides a gentle coverage of the theory of nonlinear expectations and related stochastic analysis. Many notions and results, for example, G-normal distribution, G-Brownian motion, G-Martingale representation theorem, and related stochastic calculus are first introduced or obtained by the author. This book is based on Shige Peng’s lecture notes for a series of lectures given at summer schools and universities worldwide. It starts with basic definitions of nonlinear expectations and their relation to coherent measures of risk, law of large numbers and central limit theorems under nonlinear expectations, and develops into stochastic integral and stochastic calculus under G-expectations. It ends with recent research topic on G-Martingale representation theorem and G-stochastic integral for locally integrable processes. With exercises to practice at the end of each chapter, this book can be used as a graduate textbook for students in probability theory and mathematical finance. Each chapter also concludes with a section Notes and Comments, which gives history and further references on the material covered in that chapter. Researchers and graduate students interested in probability theory and mathematical finance will find this book very useful.
650 0 $a Probabilities. $3 527847
650 0 $a Economics, Mathematical . $3 1253712
650 1 4 $a Probability Theory and Stochastic Processes. $3 593945
650 2 4 $a Quantitative Finance. $3 669372
710 2 $a SpringerLink (Online service) $3 593884
773 0 $t Springer Nature eBook
776 0 8 $i Printed edition: $z 9783662599020
776 0 8 $i Printed edition: $z 9783662599044
776 0 8 $i Printed edition: $z 9783662599051
830 0 $a Probability Theory and Stochastic Modelling, $x 2199-3130 ; $v 76 $3 1254049
856 4 0 $u https://doi.org/10.1007/978-3-662-59903-7
912 $a ZDB-2-SMA
912 $a ZDB-2-SXMS
950 $a Mathematics and Statistics (SpringerNature-11649)
950 $a Mathematics and Statistics (R0) (SpringerNature-43713)